A note on M. Soares’ bounds
We give an intersection theoretic proof of M. Soares’ bounds for the Poincaré-Hopf index of an isolated singularity of a foliation of .
A note on Markov operators and transition systems
On a compact metric space X one defines a transition system to be a lower semicontinuous map . It is known that every Markov operator on C(X) induces a transition system on X and that commuting of Markov operators implies commuting of the induced transition systems. We show that even in finite spaces a pair of commuting transition systems may not be induced by commuting Markov operators. The existence of trajectories for a pair of transition systems or Markov operators is also investigated.
A note on minimal dynamical systems
A note on mixing properties of invertible extensions.
A note on pseudo-Anosov maps with small growth rate.
A note on stable iterated function systems.
A note on strange nonchaotic attractors
For a class of quasiperiodically forced time-discrete dynamical systems of two variables (θ,x) ∈ with nonpositive Lyapunov exponents we prove the existence of an attractor Γ̅ with the following properties: 1. Γ̅ is the closure of the graph of a function x = ϕ(θ). It attracts Lebesgue-a.e. starting point in . The set θ:ϕ(θ) ≠ 0 is meager but has full 1-dimensional Lebesgue measure. 2. The omega-limit of Lebesgue-a.e point in is , but for a residual set of points in the omega limit is the...
A note on the asymptotics of perturbed expanding maps.
A note on the centralizer of topological isometric extensions
The centralizer of a semisimple isometric extension of a minimal flow is described.
A note on the construction of nonsingular Gibbs measures
We give a sufficient condition for the construction of Markov fibred systems using countable Markov partitions with locally bounded distortion.
A note on the entropy of a doubly stochastic operator
We investigate the properties of the entropy and conditional entropy of measurable partitions of unity in the space of essentially bounded functions defined on a Lebesgue probability space.
A note on the fundamental matrix of variational equations in
The paper is devoted to the question whether some kind of additional information makes it possible to determine the fundamental matrix of variational equations in . An application concerning computation of a derivative of a scalar Poincaré mapping is given.
A note on the global attractivity of a discrete model of Nicholson's blowflies.
A note on the reducibility of linear differential equations with quasiperiodic coefficients.
A note on the rotationally symmetric SO(4) Euler rigid body.
A note on the structure of quadratic Julia sets
In a series of papers, Bandt and the author have given a symbolic and topological description of locally connected quadratic Julia sets by use of special closed equivalence relations on the circle called Julia equivalences. These equivalence relations reflect the landing behaviour of external rays in the case of local connectivity, and do not apply completely if a Julia set is connected but fails to be locally connected. However, rational external rays land also in the general case. The present...
A note on the Uzawa-Lucas model with unskilled labor.
A note on unimodal mappings with infinitely many attractors
A note on uniqueness of Cauchy problems associated to planar Hamiltonian systems.
A note on γ-radonifying and summing operators
In this note, we discuss certain generalizations of γ-radonifying operators and their applications to the regularity for linear stochastic evolution equations on some special Banach spaces. Furthermore, we also consider a more general class of operators, namely the so-called summing operators and discuss the application to the compactness of the heat semi-group between weighted -spaces.